Univariate Analysis

Why this matters

Univariate analysis is the fastest way to understand a single column: its typical values, spread, shape, and issues. Data Analysts use it to catch data quality problems early and to pick the right transformations before modeling or reporting.

• Real tasks it powers: sanity-check new datasets, define bins for dashboards, choose outlier rules, set thresholds for alerts, and decide how to impute missing values.
• Outcome: cleaner data, clearer visuals, and fewer surprises later in analysis.

Concept explained simply

Univariate analysis looks at one variable at a time. You summarize, visualize, and judge quality for that one column.

• Numeric (continuous/discrete): mean/median/mode, min–max, range, variance/std, IQR, percentiles, skewness; visuals: histogram, boxplot.
• Categorical: counts, proportions, mode, unique count (cardinality); visuals: bar chart.
• Date/time: counts by period (day/week/month), min/max date, gaps; visuals: line or bar by time bucket.

Mental model

Imagine a bright flashlight on a single column. Your job: identify its type, clean it, summarize it, visualize it, interpret it, then decide the next action.

• Type → Clean → Summarize → Visualize → Interpret → Decide

Standard workflow you can reuse

1. Identify variable type: numeric, categorical, date/time, or ID-like.
2. Quality check: missing %, invalid values (e.g., negatives for ages), duplicates (if ID), mixed types.
3. Summaries:
   • Numeric: count, missing %, mean, median, std, IQR, p1/p5/p95/p99, min/max, skew.
   • Categorical: unique count, top categories, proportions, rare-category tail.
   • Date/time: coverage window, gaps, counts by period.
4. Simple visuals (mentally or with tools): histogram or bar chart; boxplot for outliers.
5. Decide actions: impute, drop, winsorize, transform (log/sqrt), bin, group rare categories, or mark as ID.

Worked examples

Example 1: Numeric (Customer Age)

Sample ages: 18, 19, 20, 22, 23, 23, 24, 24, 24, 25, 26, 27, 28, 41

• Median: sort and take middle → median = 24
• IQR: Q1 ≈ 22, Q3 ≈ 26 → IQR = 4
• Outlier bounds: [Q1 − 1.5×IQR, Q3 + 1.5×IQR] = [16, 32]
• 41 is above 32 → potential outlier. Decide: verify (age 41 is valid). Keep; maybe winsorize if needed for modeling.

Example 2: Categorical (Device Type)

Counts: Mobile=610, Desktop=290, Tablet=80, Other=20 (total=1000)

• Proportions: 61%, 29%, 8%, 2%
• Decision: Group categories < 3% into "Other" to declutter charts. Keep original raw values in data.
• Mode: Mobile

Example 3: Numeric with skew (Order Value in $)

Values (n=10): 8, 10, 11, 12, 12, 13, 14, 16, 90, 120

• Mean = 30.6; Median = 12.5 → heavy right skew.
• IQR (Q1≈11, Q3≈16) → IQR=5; upper bound= Q3+1.5×IQR = 23.5 → 90 and 120 are outliers.
• Action options:
  • Report typical value as median (12.5) with IQR.
  • Use log transform for modeling: log1p(x) to stabilize variance.
  • Winsorize at p99 for robust aggregates if business-approved.

Hands-on exercises

Do these quick tasks. Compare with solutions below. Then take the quick test at the end.

Exercise 1 (ex1): Numeric — summarize and flag outliers

Data (Revenue $): 12, 13, 15, 16, 16, 18, 19, 20, 22, 25, 100, null, 14

• Tasks:
  • Compute count (incl. missing), missing %, mean, median, Q1, Q3, IQR, min, max.
  • Flag outliers using 1.5×IQR rule.
  • Recommend: median/IQR or mean/std for reporting? Briefly justify.

Exercise 2 (ex2): Categorical — proportions and grouping

Data (Signup Source counts, total 1,200): SEO=480, Paid=300, Direct=210, Referral=90, Social=60, Other=60

• Tasks:
  • Compute proportions (%) for each category.
  • Apply a 3% threshold to group rare categories into "Other". Which categories get grouped?
  • Report the new distribution after grouping.

Checklist — fast univariate QA

• Variable type identified correctly
• Missing % computed; plan to handle NA
• For numeric: median, IQR, p1/p99 checked; outliers flagged
• For categorical: top categories listed; tail reviewed
• Date range and gaps assessed (if applicable)
• Transform or binning decision recorded
• Business sanity check performed

Common mistakes and how to self-check

• Using mean/std for skewed data → Check mean vs median; if far apart, prefer median/IQR.
• Treating IDs as numeric → If unique count ≈ row count, don’t compute numeric stats.
• Ignoring missingness → Always compute missing % and decide: drop, impute, or keep as signal.
• Over-pruning categories → Keep business-critical categories even if rare.
• One-size-fits-all outlier rules → Validate with domain context (e.g., $0 sales days on holidays).

Practical projects

• E-commerce single-column audit: For 10 key columns (price, quantity, discount, device, country, date), produce a one-pager per column with summaries, plots (if available), and decisions.
• Churn dataset triage: Evaluate each variable univariately to decide: keep, transform, or drop. Document rationale.
• Automated univariate report: Build a script/notebook that outputs summaries (including missing %, percentiles, top categories) for any dataset.

Who this is for, prerequisites, learning path

Who this is for

• Data Analysts, Product Analysts, and anyone preparing datasets for reporting or modeling.

Prerequisites

• Basic statistics: mean, median, percentiles
• Comfort with spreadsheets or a scripting language (Python/R) is helpful but not required

Learning path

• Start: Univariate analysis (this page)
• Next: Bivariate analysis (relationships)
• Then: Multivariate exploration and feature engineering

Mini challenge

You receive a new column: session_duration_sec with 15% missing, min=0, p50=45, p95=900, max=7200. In 3 bullets, state your reporting metric, outlier handling, and any transform. Keep it crisp.

Next steps

• Apply this workflow to two columns in your current dataset: one numeric and one categorical.
• Document one transformation decision and its reason.
• Proceed to bivariate analysis once you can complete the checklist in under 5 minutes per column.

Quick test

Anyone can take the test. If you are logged in, your progress will be saved.